Sentence examples for bis free from inspiring English sources

The low yield of 6 (~12%) was attributed to the monometalation process, giving a mixture of starting bis(free base) porphyrin 4, the desired monozinc complex 5, and dizinc complex.

We introduce two 2-variables transforms: the partial bi-free S-transform and the partial bi-free T-transform.

We develop an analytic machinery to study Voiculescu's bi-free partial S-transform and then use the results to characterize the multiplicative bi-free infinite divisibility.

In this paper, the notion of conditionally bi-free independence for pairs of faces is introduced.

These transforms are the analogues for the bi-multiplicative and, respectively, for the additive multiplicative bi-free convolution of the 2-variables partial bi-free R-transform in our previous paper in this series.

In particular, a conditionally bi-free partial R-transform is constructed and a conditionally bi-free analogue of the Lévy Hinčin formula for planar Borel probability measures is derived.

Furthermore, limit theorems for the additive conditionally bi-free convolution are studied using both combinatorial and analytic techniques.

We use these formulas in order to prove several results about atoms of bi-free additive convolutions.

In this paper we study some analytic properties of bi-free additive convolution, both scalar- and operator-valued.

Oxygen isotope exchange experiments indicated that the lattice oxygen mobility in the Bi-doped catalysts were much higher than that in the Bi-free ones.

We show that using properties of Voiculescu's subordination functions associated to free additive convolution of operator-valued distributions, simpler formulas for bi-free convolutions can be derived.